Answer: The vectors are linearly dependent.
The solution is in the attachment
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(a) A suitable probability app tells you the probability of being less than 17,900 or more than 18,100 is about 4.55%.
(b) We want to find σ² such that 2P((18100-18000)/σ) ≤ 0.01. We use a factor of 2 because we want to count deviations both above and below 100 feet from the mean altitude. A suitable probability app can tell you the z-score such that P(Z)≤0.005, so we need to compute σ² = (100/Z)² from that result. Doing so, we get σ² ≈ 1507.
